Closure operators in the categories of modules Part II (Hereditary and cohereditary operators)
This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category \(R\)-Mod are described. Using the results of [1], in this part the other classes of closure operators \(C\) are characterized by the associated functions \(\mathcal...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/757 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-7572018-04-26T01:26:05Z Closure operators in the categories of modules Part II (Hereditary and cohereditary operators) Kashu, A. I. ring, module, preradical, closure operator, dense submodule, closed submodule, hereditary ( cohereditary) closure operator 16D90, 16S90, 06B23 This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category \(R\)-Mod are described. Using the results of [1], in this part the other classes of closure operators \(C\) are characterized by the associated functions \(\mathcal{F}_1^C\) and \(\mathcal{F}_2^{C}\) which separate in every module \(M \in R\)-Mod the sets of \(C\)-dense submodules and \(C\)-closed submodules. This method is applied to the classes of hereditary, maximal, minimal and cohereditary closure operators. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/757 Algebra and Discrete Mathematics; Vol 16, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/757/286 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
ring module preradical closure operator dense submodule closed submodule hereditary ( cohereditary) closure operator 16D90 16S90 06B23 |
| spellingShingle |
ring module preradical closure operator dense submodule closed submodule hereditary ( cohereditary) closure operator 16D90 16S90 06B23 Kashu, A. I. Closure operators in the categories of modules Part II (Hereditary and cohereditary operators) |
| topic_facet |
ring module preradical closure operator dense submodule closed submodule hereditary ( cohereditary) closure operator 16D90 16S90 06B23 |
| format |
Article |
| author |
Kashu, A. I. |
| author_facet |
Kashu, A. I. |
| author_sort |
Kashu, A. I. |
| title |
Closure operators in the categories of modules Part II (Hereditary and cohereditary operators) |
| title_short |
Closure operators in the categories of modules Part II (Hereditary and cohereditary operators) |
| title_full |
Closure operators in the categories of modules Part II (Hereditary and cohereditary operators) |
| title_fullStr |
Closure operators in the categories of modules Part II (Hereditary and cohereditary operators) |
| title_full_unstemmed |
Closure operators in the categories of modules Part II (Hereditary and cohereditary operators) |
| title_sort |
closure operators in the categories of modules part ii (hereditary and cohereditary operators) |
| description |
This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category \(R\)-Mod are described. Using the results of [1], in this part the other classes of closure operators \(C\) are characterized by the associated functions \(\mathcal{F}_1^C\) and \(\mathcal{F}_2^{C}\) which separate in every module \(M \in R\)-Mod the sets of \(C\)-dense submodules and \(C\)-closed submodules. This method is applied to the classes of hereditary, maximal, minimal and cohereditary closure operators. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/757 |
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AT kashuai closureoperatorsinthecategoriesofmodulespartiihereditaryandcohereditaryoperators |
| first_indexed |
2024-04-12T06:25:23Z |
| last_indexed |
2024-04-12T06:25:23Z |
| _version_ |
1796109238294020096 |